A uniform electric field of magnitude 320 V/m is directed in the negative y direction. The coordinates of point A are (-0.300, -0.450) m, and those of point B are (0.650, 0.300) m. Calculate the electric potential difference VB − VA.
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To calculate the electric potential difference (VB − VA) between point A and point B, we need to find the electric potential at each point and then subtract them.
Electric potential (V) is given by the equation V = Ed, where E is the magnitude of the electric field and d is the distance of the point from the reference point where the electric potential is taken to be zero.
First, let's find the electric potential at point A:
- Given: Electric field magnitude (E) = 320 V/m
- Distance from the reference point to point A (dA) = sqrt((-0.300)^2 + (-0.450)^2) = 0.540 m (using the distance formula)
- The electric potential at point A (VA) = E * dA = 320 V/m * 0.540 m
Now, let's find the electric potential at point B:
- Distance from the reference point to point B (dB) = sqrt((0.650)^2 + (0.300)^2) = 0.722 m
- The electric potential at point B (VB) = E * dB = 320 V/m * 0.722 m
Finally, we can calculate the electric potential difference VB − VA:
VB − VA = E * dB - E * dA
With the given values, you can substitute them into the equation and perform the calculation to obtain the electric potential difference VB − VA.